Multiply the following complex numbers, marked as blue dots on the graph: $( e^{\pi i / 12}) \cdot (2 e^{13\pi i / 12})$ (Your current answer will be plotted in orange.)
Explanation: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $ e^{\pi i / 12}$ ) has angle $\frac{1}{12}\pi$ and radius $1$ The second number ( $2 e^{13\pi i / 12}$ ) has angle $\frac{13}{12}\pi$ and radius $2$ The radius of the result will be $1 \cdot 2$ , which is $2$ The angle of the result is $\frac{1}{12}\pi + \frac{13}{12}\pi = \frac{7}{6}\pi$ The radius of the result is $2$ and the angle of the result is $\frac{7}{6}\pi$.